I am supposed to convert the model to binary. I'm thinking of using a Xij format, though I am not really sure how to constrain it. Any ideas? Thank you.

Since and and integer, we know . So we can write

where a, b, ..., h are binary variables (0 or 1). Making these substitutions for and in the original problem converts it to a problem in which all the variables are either 0 or 1, i.e. a binary problem.